A building drum for building first-stage, steel-reinforced, radial monoply, pneumatic tire carcasses, is disclosed. The drum comprises a circumferential array of drum-forming segments which are supported for radial displacement to and from contracted and expanded dispositions, and apparatus for displacing the segments radially between the contracted and expanded dispositions. Each of the segments has the same axial extent and terminates at each end in a respective flange projecting radially inwardly. Each of the flanges has a respective recess exposed radially outwardly, corresponding ones of the recesses which are at the same segment end defining co-operatively with one another at each such segment end a radially outwardly exposed annular bead-seat. The segments, when in a fully contracted disposition, present a substantially cylindrical outer carcass-ply support-surface having a diameter which is less than the inner diameter of any annular metallic bead-core to be thereby operated upon.